UPDATE 1-German states data point to lower Dec inflation

(Adds data from final two states)

BERLIN, Dec 30 (Reuters) - German annual inflation probably slowed for a fifth month running in December due largely to plunging fuel costs, suggesting price pressures in the broader euro zone may have eased, data from six states showed.

The annual inflation rate slowed in five of six key states that reported their data and was unchanged in a sixth.

Germany's national gauge of consumer prices (CPI), based on the data from the six key states, is due later on Tuesday.

Annual inflation in Bavaria slowed to 1.3 percent from 1.5 percent in November, and to 1.4 percent from 1.6 percent in Baden-Wuerttemberg, state statistics offices said on Tuesday.

Earlier on Tuesday, Brandenburg reported its annual inflation slowed to 1.0 percent from 1.2 percent in November, and North Rhine-Westphalia announced a slowing to 1.0 percent from 1.1 percent. In Hesse the annual inflation rate was 1.0 percent, unchanged from November.

On Monday, Saxony led the way by reporting its annual inflation rate slowed to 1.3 percent in December from 1.7 percent in November.

In all six states heating oil prices were down sharply in December. Fuel for motor transport was also lower.

Data from German states provide an important early insight into inflation trends across the euro zone. In Slovenia, inflation slowed to 1.8 percent year-on-year in December from 2.9 percent in November, the statistics office said on Tuesday.

For Germany, a Reuters poll forecast the national CPI would rise 0.4 percent on the month, with the annual inflation rate expected to slow to 1.2 percent from 1.4 percent in November.

The EU-harmonised price index (HICP) was also seen rising by 0.4 percent on the month. Prices were tipped to rise 1.2 percent on the year -- down from 1.4 percent in the previous month. (Reporting by Erik Kirschbaum; editing by David Stamp/Tony Austin)